MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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The Venn diagram below shows the 8 students in Mr. Parker’s class. The diagram shows the memberships for the Volleyball Club and the Spanish Club.

Note that "Austin" is outside the circles since he is not a member of either club.

One student from the class is randomly selected.
Let \( A \) denote the event "the student is in the Volleyball Club."
Let \( B \) denote the event "the student is in the Spanish Club."

Answer each part below. If necessary, consult a list of formulas.

**Venn Diagram Explanation:**
- **Volleyball Club**: Circle on the left with members: Mai, Jose, Felipe
- **Spanish Club**: Circle on the right with members: Jose, Felipe, Keith, Keiko, Lisa, Lamar
- **Overlap (Both Clubs)**: Jose, Felipe
- **Outside Both Circles**: Austin

**Task (a):** Find the probabilities of the events below. Write each answer as a single fraction.

- \( P(A) = \) \(\_\)
- \( P(B) = \) \(\_\)
- \( P(A \text{ and } B) = \) \(\_\)
- \( P(A \text{ or } B) = \) \(\_\)
- \( P(A) + P(B) - P(A \text{ and } B) = \) \(\_\)

**Task (b):** Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \).

- \( \circ P(A) \)
- \( \circ P(A \text{ and } B) \)
- \( \circ P(A \text{ or } B) \)
- \( \circ P(B) \)
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Transcribed Image Text:The Venn diagram below shows the 8 students in Mr. Parker’s class. The diagram shows the memberships for the Volleyball Club and the Spanish Club. Note that "Austin" is outside the circles since he is not a member of either club. One student from the class is randomly selected. Let \( A \) denote the event "the student is in the Volleyball Club." Let \( B \) denote the event "the student is in the Spanish Club." Answer each part below. If necessary, consult a list of formulas. **Venn Diagram Explanation:** - **Volleyball Club**: Circle on the left with members: Mai, Jose, Felipe - **Spanish Club**: Circle on the right with members: Jose, Felipe, Keith, Keiko, Lisa, Lamar - **Overlap (Both Clubs)**: Jose, Felipe - **Outside Both Circles**: Austin **Task (a):** Find the probabilities of the events below. Write each answer as a single fraction. - \( P(A) = \) \(\_\) - \( P(B) = \) \(\_\) - \( P(A \text{ and } B) = \) \(\_\) - \( P(A \text{ or } B) = \) \(\_\) - \( P(A) + P(B) - P(A \text{ and } B) = \) \(\_\) **Task (b):** Select the probability that is equal to \( P(A) + P(B) - P(A \text{ and } B) \). - \( \circ P(A) \) - \( \circ P(A \text{ and } B) \) - \( \circ P(A \text{ or } B) \) - \( \circ P(B) \)
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